Light and Optics

Practice Problems

1. 1997B5 An object is placed 30 mm in front of a lens. An image of the object is located 90 mm behind the lens.

(a) Is the lens converging or diverging? Explain your reasoning.

(b) What is the focal length of the lens?

(c) On the axis below, draw the lens at position x = 0. Draw at least two rays and locate the image to show the situation described above.

(d) Based on your diagram in (c), describe the image by answering the following questions in the blank spaces provided.

Is the image real or virtual?

Is the image smaller than, larger than, or same size as the object?

Is the image inverted or upright compared to the object?

(e) The lens is replaced by a concave mirror of focal length 20 mm. On the axis below, draw the mirror at position x = O so that a real image is formed. Draw at least two rays and locate the image to show this situation.

2. 1994B5 A point source S of monochromatic light is located on the bottom of a swimming pool filled with water to a depth of 1.0 meter, as shown above. The index of refraction of water is 1.33 for this light. Point P is located on the surface of the water directly above the light source. A person floats motionless on a raft so that the surface of the water is undisturbed.

(a) Determine the velocity of the source's light in water.

(b) On the diagram above, draw the approximate path of a ray of light from the source S to the eye of the person. It is not necessary to calculate any angles.

(c) Determine the critical angle for the air-water interface.

3. 2000B4 (15 points)

A sheet of glass has an index of refraction ng = 1.50. Assume that the index of refraction for air is na= 1.00.

(a)Monochromatic light is incident on the glass sheet, as shown in the figure below, at an angle of incidence of 60. On the figure, sketch the path the light takes the first time it strikes each of the two parallel surfaces. Calculate and label the size of each angle (in degrees) on the figure, including angles of incidence, reflection, and refraction at each of the two parallel surfaces shown.


(b) Next a thin film of material is to be tested on the glass sheet for use in making reflective coatings. The film has an index of refraction nf= 1.38. White light is incident normal to the surface of the film as shown below. It is observed that at a point where the light is incident on the film, light reflected from the surface appears green ( = 525 nm).

  1. What is the frequency ofthe green light in air?
  1. What is the frequency ofthe green lightin the film?
  1. What is the wavelength of the green light in the film?
  1. Calculate the minimum thickness of film that would produce this green reflection.

4. 1991B6

Light consisting of two wavelengths, a = 4.4 x 10-7 meter and b 5.5 x 10-7 meter, is incident normally on a barrier with two slits separated by a distance d. The intensity distribution is measured along a plane that is a distance L = 0.85 meter from the slits, as shown above. The movable detector contains a photoelectric cell whose position y is measured from the central maximum. The first-order maximum for the longer wavelength b occurs at b 1.2 x 10-2 meter.

(a) Determine the slit separation d.

(b) At what position y, does the first-order maximum occur for the shorter wavelength a?

In a different experiment, light containing many wavelengths is incident on the slits. It is found that the photosensitive surface in the detector is insensitive to light with wavelengths longer than 6.0 x 10-7 m.

(c) Determine the work function of the photosensitive surface.

(d) Determine the maximum kinetic energy of electrons ejected from the photosensitive surface when exposed to light of wavelength  = 4.4 x 10-7 m.